I've read that Mussolini acted a mentor to Hitler when he first came to power but Hitler soon eclipsed Mussolini and became the mentor. I have also heard that Mussolini became more and more discouraged as the war went on, and that he eventually got into an argument with Hitler at a meeting because he could no longer tolerate Hitler's boasting.
Your description is accurate. Hitler based many of his ideas and mannerisms on Mussolini's. In private Hitler professed admiration for Mussolini, however, Mussolini wasn't as kind and would badmouth Hitler in private. He claimed that Mien Kampf was a boring, worthless book, and he criticized Hitler's ideas as simplistic. A rather funny event was the meeting in Venice between the two in 1934. Mussolini was subjected to some of Hitler's infamous long rants and quickly grew bored. The summit with both men thinking much less of each other. They also disagreed over racial policy as Mussolini wasn't nearly as anti Semitic as Hitler was and Mussolini thought the idea of a "master" race was stupid (though eventually he was influenced into passing racial laws). Mussolini also early on was more than willing to stab Hitler in the back if it advanced the Italian agenda (he was a staunch nationalist, and it influenced him much more than any political leaning).
You raised the point about how Mussolini became more and more discouraged because of the war's progress. This is true. Mussolini knew his country would not be able to fight a war effectively, but he assumed it would be a quick affair and so he joined the axis. However, Mussolini was only truly broken when he was forced to head the Italian puppet state, the SRI under threat from Hitler. He knew he was little more than a puppet and this(along with the destruction of Italy) destroyed him on the inside. For example in an interview in 1945 he stated that he felt that he was little more than a corpse.
Source:
Mussolini by Dennis Smith
Mussolini: The Last 600 Days of Il Duce By Ray Moseley